Réitigh 3/sqrt{5}(2sqrt{2}-sqrt{3})(sqrt{2}+2sqrt{3})-sqrt{24}

$$\frac { 3 } { \sqrt { 5 } } ( 2 \sqrt { 2 } - \sqrt { 3 } ) ( \sqrt { 2 } + 2 \sqrt { 3 } ) - \sqrt { 24 }$$

Luacháil

$$\frac{9\sqrt{30}}{5}-\frac{6\sqrt{5}}{5}-2\sqrt{6}\approx 2.276744977$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{5} chun ainmneoir \frac{3}{\sqrt{5}} a thiontú in uimhir chóimheasta.

$$\frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)-\sqrt{24}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$\frac{3\sqrt{5}}{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)-\sqrt{24}$$

Scríobh \frac{3\sqrt{5}}{5}\left(2\sqrt{2}-\sqrt{3}\right) mar chodán aonair.

$$\frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)}{5}\left(\sqrt{2}+2\sqrt{3}\right)-\sqrt{24}$$

Scríobh \frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)}{5}\left(\sqrt{2}+2\sqrt{3}\right) mar chodán aonair.

$$\frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)}{5}-\sqrt{24}$$

Fachtóirigh 24=2^{2}\times 6. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 6} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{6}. Tóg fréamh chearnach 2^{2}.

$$\frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)}{5}-2\sqrt{6}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh -2\sqrt{6} faoi \frac{5}{5}.

$$\frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)}{5}+\frac{5\left(-2\right)\sqrt{6}}{5}$$

Tá an t-ainmneoir céanna ag \frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)}{5} agus \frac{5\left(-2\right)\sqrt{6}}{5} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)+5\left(-2\right)\sqrt{6}}{5}$$

Déan iolrúcháin in 3\sqrt{5}\left(2\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+2\sqrt{3}\right)+5\left(-2\right)\sqrt{6}.

$$\frac{12\sqrt{5}+12\sqrt{30}-3\sqrt{30}-18\sqrt{5}-10\sqrt{6}}{5}$$

Déan áirimh in 12\sqrt{5}+12\sqrt{30}-3\sqrt{30}-18\sqrt{5}-10\sqrt{6}.

$$\frac{-6\sqrt{5}-10\sqrt{6}+9\sqrt{30}}{5}$$